Algorithms for Quadratic Matrix and Vector Equations

by Federico Poloni

Overview

This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. These equations appear, in different forms, in several practical applications, especially in applied probability and control theory. The equations are first presented using a novel unifying approach; then, specific numerical methods are presented for the cases most relevant for applications, and new algorithms and theoretical results developed by the author are presented. The book focuses on “matrix multiplication-rich” iterations such as cyclic reduction and the structured doubling algorithm (SDA) and contains a variety of new research results which, as of today, are only available in articles or preprints.

Product Details

ISBN-13:	9788876423833
Publisher:	Scuola Normale Superiore
Publication date:	01/26/2012
Series:	Publications of the Scuola Normale Superiore , #16
Edition description:	2011
Pages:	250
Product dimensions:	6.61(w) x 9.45(h) x 0.04(d)

Table of Contents

Linear algebra preliminaries.– Quadratic vector equations.– A Perron vector iteration for QVEs.– Unilateral quadratic matrix equations.– Nonsymmetric algebraic Riccati equations.– Transforming NAREs into UQMEs.– Storage optimal algorithms for Cauchy-like matrices.– Newton method for rank-structured algebraic Riccati equations.– Lur'e equations.– Generalized SDA.– An effective matrix geometric mean.– Constructing other matrix geometric means.